Controlling for individual differences in a repeated-measures design?

Question

I have been analysing a study where around 500 participants each were given a survey, so there were repeated measurements of each participant. Participants were male and female uni students who were presented with 4 character descriptions differing on gender (male/female) and health behavior (healthy/unhealthy), which they had to judge on, for example, weakness. Analyses I have conducted are paired-sample t-tests and two-way repeated measures ANOVAs. Now my supervisors want me to add control variables into the analysis, namely; participant gender, participant SES, participant sexual orientation, etc. by using an ANCOVA. However, I keep finding that all these individual differences in the participants are already controlled for by design, as repeated-measures ANOVA is an analysis within subjects thus individual differences don't play a role. This would mean that significance I have found now is valid and not confounded by the individual characteristics of the participants. Is this correct?

However, then I am confused on how to see whether the effect of the vignette on the dependent variable (e.g., weakness) differs according to participant gender and so on. Do I have to use a mixed ANOVA for this?

For clarification: Each participant read 4 vignettes with character descriptions, these descriptions depicted 2 x 2 manipulated actor variables: health behavior (healthy or unhealthy) x gender (male or female). So these were the independent variables, two categorical within-subject factors. Dependent variables were measured per vignette, for example, the weakness dependent variable was measured by averaging the scores on 4 Likert items (e.g., "To what extent does this person come across as insecure?"). Also, participant characteristics were measured (age, gender, health behavior, education, etc.). Chunck of data:

PpNr = Participant number, Weak_C1X = Average weakness judgment of healthy male, Weak_C2X = Average weakness judgment of unhealthy male, Weak_C3X = Average weakness judgment of healthy female, Weak_C4X = Average weakness judgment of unhealthy female, SES = Socio-economic status of participant, Age = Age of participant, Gender = Gender of participant

Answer 1

It's not totally clear from your description what is your dependent variable that you analyze, but let's assume it's some continuous variable and you've measured it in three different situations. Let's say that's before the study starts, during the study when participants have received their first intervention and during the study when participants have received their second intervention, where there's two interventions and for each participants we randomly do A or B first followed by the other one.

One plausible analysis here is to fit a mixed effects model to only the on-intervention outcomes adjusted for the pre-intervention outcome such as (using R notation):

lme4::lmer( outcome ~ 1 + intervention + timepoint + pre_intervention_outcome + timepoint:pre_intervention_outcome + (1|Subject) )

One thing that happens here is that there's a random-subject effect on the intercept due to + (1|Subject) that says there's between-subject variation beyond what is explained by having the pre_intervention_outcome + timepoint:pre_intervention_outcome terms of the model. However, there usually will be remaining residual variation, which maybe could be explained by other explanatory variables like e.g. gender. One could adjust for that just as for the pre-intervention outcome. If one does not adjust for that, the extra unexplained variability is being absorbed into between subject or within subject variation.

With more timepoints, it becomes relevant to discuss how timepoints could be correlated. E.g. if one wants to leave that flexible something like a MMRM with an unstructured covariance matrix might be an option.